Why Investigate Root Architecture and Water Uptake?

• Spatially variable models are needed as precision agriculture takes hold. (Green et al., 2006)
• 3D models coupling soil waterflow and root uptake could be used to test hypotheses of root permeability, architecture adapatiation, and genotypic affects on uptake and solute transport. (Dorlodot et al., 2007)
• 3D models may help develop better 1D models.
• Roots play a large role in plant productivity, especially under stress.(Lynch, 1995)

Theory & History

• Root-Soil Water Movement and Solute Model (R-SWMS)
  • Coupling of two models: one focused on whole root system continuinty (Somma et al., 1998) and one focused on water transfer into and within the root sytem (Doussan et al., 1998)
• Richard’s Equation
• One-Dimensional vs Two-Dimensional vs Three-Dimensional
  • Processing power: How many parameters is too many?
• 3D models can tackle some major issues:
  • Different roots have different functions.
  • Soil water content is heterogeneous.
  • Water uptake is a passive process.

Root-Soil Water Movement and Solute Model (R-SWMS)

• The root-soil water movement and solute model is used to describe the flow of water and nutrients based on gradients towards the root collar.
• The authors hope to develop it further to tackle questions involving root water uptake and flow, nutrient uptake and flow, but will start with some basic questions.
• This requires MANY assumptions.

Richard’s Equation

• The equation is used to describe water flow under unsaturated conditions. It relates water flow based on the gradients caused by matric and gravitational potential, and we add “sink terms” when incorporating root water uptake.

• \(\frac{\partial \theta}{\partial t} = \nabla \cdot [\textbf{K} \nabla(h-z)] - S\)
  
  
  • \(\theta =\) volumetric water content
  • \(t =\) time
  • \(\textbf{K} =\) hydraulic conductivity tensor
  • \(h =\) water pontential on a weight basis
  • \(S =\) sink term representing root water uptake
  • \(z =\) vertical coordinate

Solving Richard’s Equation

• They discretize the root system as a network of connected root nodes.
  
  
• Radial Flow (Soil-Root):
  • \(J_{r} = K_{r}^{*}s_{r}[h_{s}(z)-h_{x}(z)]\)
• Axial Flow (Xylem):
  • \(J_{x} = -K_{x}(\frac{\Delta h_{x}}{l} + \frac{\Delta z}{l})\)
    
    
    • \(K_{r}^{*} =\) intrinsic radial conductivity
    • \(K_{x} =\) xylem conductivity
    • \(h_{s} =\) water potential at the root surface
    • \(h_{x} =\) water potential in the xylem
    • \(s_{r} =\) outer surface of the root segment
    • \(l =\) length of the root segment
    • \(z =\) vertical coordinate
      
      
• These are only valid under normal conditions: no extreme water stress.

Solving Richard’s Equation Cont.

• Iteratively solve the soil and root network flow equations for water flow.
• Since water flow and root network flow are linked by the radial flux equation, they solve \(J_{r}\) for each root segment in a voxel, and sum them to find the sink term for that voxel.

• They can then use this voxel sink term to solve for water flow by voxel.

• \(S_{j} = \frac{\sum\limits_{i}^{n_{i}}{J_{r,i}}}{V_{j}}\)
  
  
  • \(J_{r,i} =\) Radial flow for root segment i
  • \(V_{j} =\) voxel volume: going to be \(1 \ cm^3\)
  • \(n_{i} =\) number of root segments within voxel j
    
    
    
• Model is first solved based on initial soil water potential (\(h_{s}\))
  • Obtained from distance-weighted average of soil water potential at the corners of the soil voxels including root segments.

The Assumptions

• What are the assumptions?
  
  

1. Soil water is preferably taken up at spatial locations where the energy to bring water to the root collar is minimized.
2. Osmotic potential is negligible and root water capacity can be neglected.
   1. Valid under “normal” conditions. What about water stress?
3. Soil and root parameters are constant and uniform.
4. Soil homogeneity.
5. No Root growth.
6. Root water uptake is passive.

The Questions

1. How do collar boundary conditions affect uptake?
   
   
2. How does soil texture affect uptake?
   
   
3. Which model parameters have what affect?
   
   
4. Effective sinusoidal day-night cycle?
   
   
5. Can we develop better 1D models?

Methodology: Scenarios

• Corn root structure defined with the model of Somma et al.(1998); 500h old, 9,488 root segments, homogenous soil.
• Grown in \(10cm \ \times \ 10cm \ \times \ 40cm\) column made up of \(1 \ cm^3\) voxels
• Colar Boundary Conditions (CBCs 1-3)
  • Constant Potential vs. Constant Flux vs. Sinusoidal Day-Night Fluxes.
  • No flux at the top or bottom.
  • In equilibriam with aquifer 300 cm below.

Methodology: Parameters

• Soil properties set using Mualem-van Genuchten parameters. (Genuchten and Nielsen, 1985; R.F. and Parrish, 1988)
• Conductivity drives uptake (water takes path of least resistance)
  • Multiplied soil, radial, and xylem conductivity by 10 to test model sensitivity.
  • Compared spatial distribution of sink term, soil water potential, and water content.
  • Conducted on CBCs 1 and 2.

Effects of Soil Type

• Loam has the highest moisture capacity and saturated conductivity, but the steepest decrease.
• Clay had flatter hydraulic functions and a lower capacity and saturated hydraulic conductivity.
• Clay loam exhibited intermediate hydraulic properties.
• CBC 1 and 2 used for soil texture sensitivity.

Reference Parameterization with Collar Boundary Condition 1

• 0.5 day of CBC 1
• Subplot b: \(h_{x}\) is controlled by the distance of a root segment from the collar and the number of branches in between. -Long root connected to colar will take up more water under uniform conductive properties.
• Subplot c: waterflux streamlines are not horizontal as 2D models assume
• Subplots d and e: Water is taken up in locations where gradient between bulk soil and xylem water potentials is largest. (Lower depths)

Effect of the Parameterization on the Root Collar Flux

• Principal resistance to water flow is located at radial root tissues (Steudle and Peterson, 1998)
• Xylem Conductivty >>> Radial Conductivity.
  • Changing radial conductivity will have a larger impact.
• Radial conductivity increase allows roots to access more water before soil is water limiting.
• Saturated hydraulic conductivity increase delays and smooths drying process.
  • Dependent on soil hydraulic conductivity curve (soil texture).

Effect of Parameterization on the Three-Dimensional Distribution of Water Content (CBC 1)

• Again, xylem conductivity does not play a huge role in either CBC 1 or 2.
• Radial conductivity increase affects water content distribution: this is supported by increased water flow at the root collar in figure 3.
• Saturated hydraulic conductivity increase homogenizes water distribution.

Effect of Parameterization on the Three-Dimensional Distribution of Water Content (CBC 2)

• Since colar flux is set to constant, all of the scenarios have similar water extraction.
• However, increase saturated hydraulic conductivity still homogenizes water distribution.

Effect of Parameterization on the Sink-Term Profiles

• CBC 1: Increase in radial and xylem conductivity increase water uptake, leading to a more unfiorm sink-term profile by depth.
• CBC 2: Low flow at the collar, soil governs depth distribution of root water uptake.
• Makes sense when viewing figure 4.

Effect of Parameterization on the Vertical Distribution of Water Content and Flow Velocity Field

• Redistribution changes drastically with increased \(K_{sat}\)
  • Deeper profiles compensate for changes caused by root uptake.
  • Challenges the assumption that changes in water content correspond to the sink-term profile.
  • Are flow streamlines principaly horizontal? This indicates they are not.

Effect of Parameterization on the Vertical Distribution of Water Content and Flow Velocity Field Cont.

• Cooefficients of variation for water content, horizontal and vertical components of the velocity field profile characterize the degree of water distribution heterogeneity induced by water uptake.
• Crucial for solute transport prediction at the plant scale.
• Similar to results from geophysical tomography.
  
  
• Results suggest that 3D water content maps combined with transpiration monitoring could provide insight for root-soil interactions and the relative importance of different resistances along the water flow pathway.

Effect of Soil Type

• Stress appears first in the loam, then clay, then clay-loam.
• Clay-loam extracted the most water.
• \(K_{sat}\) alone cannot predict a priori soil behavior.
  • \(K_{sat}^{loam} = 24.96 \ cm \ d^{-1}\)
  • \(K_{sat}^{clay-loam} = 6.24 \ cm \ d^{-1}\)
  • \(K_{sat}^{clay} = 4.8 \ cm \ d^{-1}\)

Effect of Soil Type Cont.

• Loam has heterogenous 3D water potential distribution surrounding main root axes.
• Loam has steeper hydraulic properties - early stress.

Effect of Soil Type Cont. 2

• Loam soils generated stress quickly.
• Clay-loam sustains the evaporative demand the longest.
• Not apparent from 1D models.
• Could 3D models change our assumptions of soil-root interactions?

Day-Night Scenario

• Sinusoidal pattern of transpiration varying from 0 to 1.563 \(cm \ d^{-1}\)
• During minimum transpiration, a negative sink term is present.
  • This represents the hydraulic lift carried out by some root systems.
  • Water is drawn up during the day and released into the upper soil profile at night to be used again the following day.
• Some plants may have mechanisms to reduce radial conductivity to avoid the release of water at night. (Vandeleur et al., 2005)
  • Should this be modeled too?
• After 9.75 days, plants started to take up water from deeper in the soil.

Effective Sink Term as a Function of Bulk Water Potential and Averaged Water Content Cont.

• Normalized the sink term by dividing by potential transpiration
  • \(S^{*}(z,t) = \frac{S(z,t)}{T_{pot}}\)
• Calculated water potential and content at each depth and plotted against this normalized sink term \(S^{*}\)
• Also plotted against the normalized sink term divided by the root surface density \(\frac{S^{*}}{RSD}\)
• These plots do not resemble those commonly used for \(\alpha_{1}\) in Feddes model (1977).
  • How many papers used a stress function that may not be robust to changes in climactic and soil conditions?

Conclusions

• Water uptake is complex. Very complex.
• High soil conductivity lowers soil variability, and cannot predict soil hydraulic properties alone.
• Retention and conductivity curves (soil texture) plays a key role in uptake.
• One dimensional models may not be robust.

What’s Missing

• The assumptions:
  • Root growth
  • Heterogeneity of soil texture
  • Heterogeneity of.. well everything
• Mycorrizhal Fungi
• Microbial Water Interactions
• Plant Interactions in the Row (including weeds)
• Intercropping
• Seasonal Effects

How Do We Fill In The Gaps?

• New Imaging Technologies
• Resonance, X-Ray, Hyperspectral
• Varied Root, Water and Nutrient Models
• Field and Container Images of Roots
• Electrical Resistance and Current
• Isotopic Tracer Experiments
  
  
• Any bright ideas?